Finite Group Databasebeta

← #25254354

Subgroups — #25254354

Order 11008.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147463C211yesmaximal, characteristic, complemented
2#19136836C211yesmaximal, characteristic, complemented
3#19136831C211yesmaximal, characteristic, complemented
4#19136826C211yesmaximal, characteristic, complemented
5#19136759C211yesmaximal, characteristic, complemented
6#19136752C211yesmaximal, characteristic, complemented
7#19136732C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136647C211yesmaximal, characteristic, complemented
10#19136627C211yesmaximal, characteristic
11#19136504C211yesmaximal, characteristic, complemented
12#19136469C211yesmaximal, characteristic, complemented
13#19136457C211yesmaximal, characteristic, complemented
14C4×#13063266C211yesmaximal, characteristic, complemented
15C43×#3396C211yesmaximal, characteristic, complemented
16#14583609—21no—
17C2×#13063268C2211yescharacteristic
18C2×#13063266C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583301C2211yescharacteristic
23#14583200—21no—
24#14583200—21no—
25#14583190—21no—
26C4×D344C2211yescharacteristic
27C4×D344C2211yescharacteristic
28C4×D344C2211yescharacteristic
29#14582726C2211yescharacteristic
30#14582724C2211yescharacteristic
31#14582724C2211yescharacteristic
32C4⋊(C43⋊C16)C2211yescharacteristic
33C4⋊(C43⋊C16)C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582703C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582700C2211yescharacteristic
39#14582700C2211yescharacteristic
40#14582700C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic
45#14582675C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#559—21no—
49C43×#495C2211yescharacteristic
50C43×#495C2211yescharacteristic
51C43×#493C2211yescharacteristic
52C43×#463—21no—
53C43×#463—21no—
54C43×#460—21no—
55C8×Q8×C43C2211yescharacteristic
56C4×Q16×C43C2211yescharacteristic
57C4×D8×C43C2211yescharacteristic
58C4×D8×C43C2211yescharacteristic
59C2×D344C2311yescharacteristic
60#13063325—21no—
61#13063317—21no—
62#13063317—21no—
63#13063303—41no—
64#13063303—41no—
65#13063301—41no—
66C4×D172—21no—
67C4×D172—21no—
68C4×D172—21no—
69C4⋊C4×D43—41no—
70#13063268—22no—
71#13063266—22no—
72#13063266—22no—
73C2×C43⋊C16C2311yescharacteristic
74C2×C43⋊C16C2311yescharacteristic
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77#13063259—21no—
78#13063259C2311yescharacteristic
79#13063259C2311yescharacteristic
80#13063259C2311yescharacteristic
81#13063257—21no—
82#13063257—21no—
83#13063247—21no—
84#13063247—21no—
85#13063247—21no—
86C2×Q16×C43C2311yescharacteristic
87C2×SD16×C43—21no—
88C2×SD16×C43—21no—
89C2×D8×C43—21no—
90C2×D8×C43C2311yescharacteristic
91C2×D8×C43C2311yescharacteristic
92#127×C43—21no—
93#124×C43—21no—
94#124×C43—21no—
95#124×C43—41no—
96#123×C43—41no—
97#123×C43—41no—
98C4×Q8×C43—21no—
99C4×Q8×C43D411yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—41no—
103#107×C43C2311yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43D411yescharacteristic
107#103×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110C4×C8×C43C2311yescharacteristic
111C4×C8×C43C2311yescharacteristic
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×Q8×C43D811yescharacteristic
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C2×D172—21no—
122C2×C4×D43—41no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C2×Dic86—41no—
126Q16×C43—21no—
127Q16×C43—21no—
128SD16×C43—81no—
129SD16×C43—81no—
130D8×C43—21no—
131D8×C43—21no—
132D8×C43—21no—
133D8×C43—21no—
134D8×C43—81no—
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2×D411yescharacteristic
138C2×C8×C43C2411yescharacteristic
139C4⋊C4×C43—21no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43D811yescharacteristic
142C4⋊C4×C43D811yescharacteristic
143C4⋊C4×C43D811yescharacteristic
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43—41no—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—41no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165D344—21no—
166D344#4112yes—
167C43⋊C16—21no—
168C43⋊C16—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C23×C43—41no—
173C22×D43—41no—
174Q8×C43—41no—
175Q8×C43—41no—
176Q8×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—41no—
180D4×C43—41no—
181D4×C43—82no—
182D4×C43—161no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—161no—
186C2×C4×C43—161no—
187C2×C4×C43C2×D811yescharacteristic
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197D172—22no—
198D172—41no—
199C4×D43—82no—
200C4×D43—161no—
201C4×D43—161no—
202Dic86—161no—
203C8×C43—21no—
204C8×C43—21no—
205C8×C43—21no—
206C8×C43C2×#4111yescharacteristic
207C8×C432−1+411yescharacteristic
208#33937—431nomaximal, Sylow
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43C22×D811yescharacteristic
216C2×D43—42no—
217C2×D43—81no—
218C2×D43—81no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—81no—
226C4×C43—81no—
227C4×C43#54811yescharacteristic
228C4×C43#57711yescharacteristic
229Dic43—81no—
230Dic43—81no—
231Dic43—81no—
232#3396D4311yescharacteristic, complemented
233#3380—431no—
234#2244—431no—
235#2243—431no—
236#2242—431no—
237#2229—431no—
238#2228—431no—
239#2224—431no—
240#2210—431no—
241#2210—431no—
242#2206—431no—
243#2183—431no—
244#2177—431no—
245#2175—431no—
246C4×D16—431no—
247C2×C43—161no—
248C2×C43—161no—
249C2×C43#335811yescharacteristic
250C2×C43#341411yescharacteristic
251C2×C43#341511yescharacteristic
252D43—82no—
253#559—21no—
254#554—861no—
255C2×SD32—431no—
256C2×D16—431no—
257C2×D16—431no—
258#500—431no—
259#499—431no—
260#499—431no—
261#495C2×D4311yescharacteristic
262#495C2×D4311yescharacteristic
263#493C2×D4311yescharacteristic
264#478—861no—
265#478—861no—
266#476—861no—
267#463—21no—
268#463—21no—
269#460—21no—
270C8×Q8C2×D4311yescharacteristic
271C4×Q16C2×D4311yescharacteristic
272C4×D8—431no—
273C4×D8—431no—
274C4×D8—431no—
275C4×D8C2×D4311yescharacteristic
276C4×D8C2×D4311yescharacteristic
277#367—431no—
278#366—431no—
279#366—431no—
280C4⋊C16—431no—
281C4⋊C16—431no—
282C4⋊C16—431no—
283#358—431no—
284#358—431no—
285#358—431no—
286#357—431no—
287#357—431no—
288#357—431no—
289#357—431no—
290#357—431no—
291#357—431no—
292#357—431no—
293#346—431no—
294#346—431no—
295C4×C16—431no—
296C43#3393711yescharacteristic, complemented, Sylow
297C2×Q16C22×D4311yescharacteristic
298C2×SD16—21no—
299C2×SD16—21no—
300C2×D8—21no—
301C2×D8—431no—
302C2×D8C22×D4311yescharacteristic
303C2×D8C22×D4311yescharacteristic
304C4⋊Q8—861no—
305#127—21no—
306#125—861no—
307#125—861no—
308#124—21no—
309#124—21no—
310#124—41no—
311#123—41no—
312#123—41no—
313C22⋊Q8—1721no—
314C22⋊Q8—1721no—
315C22⋊Q8—1721no—
316C4×Q8—21no—
317C4×Q8C22⋊D4311yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—41no—
321C4×D4—861no—
322C4×D4—861no—
323C4×D4—861no—
324C2×C4⋊C4—1721no—
325SD32—862no—
326D16—862no—
327D16—862no—
328C2×C16—431no—
329C2×C16—431no—
330C2×C16—431no—
331C2×C16—431no—
332#107—431no—
333#107—431no—
334#107—431no—
335#107—861no—
336#107C22×D4311yescharacteristic
337#106—861no—
338#106—861no—
339C4⋊C8C22⋊D4311yescharacteristic
340C4⋊C8C22⋊D4311yescharacteristic
341C4⋊C8C22⋊D4311yescharacteristic
342#103—21no—
343#102—21no—
344#102—21no—
345#102—861no—
346#102—861no—
347#102—861no—
348C4×C8C22×D4311yescharacteristic
349C4×C8C22×D4311yescharacteristic
350C4×C8C22×D4311yescharacteristic
351C2×Q8—21no—
352C2×Q8—1721no—
353C2×Q8#1062188211yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—861no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—1721no—
362C22×C4—1721no—
363C22×C4—1721no—
364Q16—21no—
365Q16—21no—
366SD16—81no—
367SD16—81no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—21no—
372D8—81no—
373D8—432no—
374D8—861no—
375C2×C8C2×C22⋊D4311yescharacteristic
376C2×C8C2×C22⋊D4311yescharacteristic
377C2×C8C2×C22⋊D4311yescharacteristic
378C2×C8C23×D4311yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C4⋊C4#1062188211yescharacteristic
390C4⋊C4#1062188211yescharacteristic
391C4⋊C4#1062188211yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C42—41no—
402C42C2×C22⋊D4311yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C42C2×C22⋊D4311yescharacteristic
405C16—861no—
406C16—861no—
407C16—861no—
408C16—861no—
409C23—41no—
410C23—41no—
411C23—1721no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—6881no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—161no—
422D4—862no—
423D4—1721no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—3442no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—6881no—
433C2×C4—6881no—
434C2×C4C2×#1062188211yescharacteristic
435C2×C4C2×#1062188211yescharacteristic
436C2×C4C2×#1062188211yescharacteristic
437C2×C4C2×#1062188211yescharacteristic
438C2×C4C2×#1062188211yescharacteristic
439C2×C4C2×#1062188211yescharacteristic
440C2×C4C22×C22⋊D4311yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8#41×D4311yescharacteristic
445C8#1306337211yescharacteristic
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—3441no—
453C22—3441no—
454C22—1722no—
455C22C22×#1062188211yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—3441no—
465C4—3441no—
466C4—3441no—
467C4#1458355611yescharacteristic
468C4#1458371011yescharacteristic
469C2—161no—
470C2—161no—
471C2—3442no—
472C2#1914722611yescharacteristic
473C2#1914772911yescharacteristic
474C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3396C2
socleC22×C43C22×D8
prime radical#19136627C2
hypercenter#3396D43
hypocenterC43#33937
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19147463C2semidirect
2. #19136836C2semidirect
3. #19136831C2semidirect
4. #19136826C2semidirect
5. #19136759C2semidirect
6. #19136752C2semidirect
7. #19136732C2semidirect
8. #19136647C2semidirect
9. #19136647C2semidirect
11. #19136504C2semidirect
12. #19136469C2semidirect
13. #19136457C2semidirect
14. C4×#13063266C2semidirect
15. C43×#3396C2semidirect
232. #3396D43semidirect
296. C43#33937semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191474632
#191368362
#191368312
#191368262
#191367592
#191367522
#191367322
#191366472
#191366272
#191365042
#191364692
#191364572
C4×#130632662
C43×#33962
#3393743